“He’s not going to sign a bill that doesn’t have money for the wall. I can tell you exactly how this is going to end. The president is going to challenge Democrats to compromise and if they continue to say no, they’re going to pay the price with the American people," Graham said during an appearance on Fox News's "Hannity."

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“If he gives in now, that’s the end of 2019 in terms of him being an effective president," he continued. "That’s probably the end of his presidency. Donald Trump has made a promise to the American people. He’s going to secure our border."

“That’s the end of us if we give in on this issue as Republicans," Graham said. "I hope Mitt Romney and everybody else knows this is a fight worth having."

Romney wrote an op-ed in The Washington Post on Tuesday criticizing Trump's character, saying he hasn't "risen to the mantle" of the presidency. But Romney also said during an interview on CNN on Wednesday that he "would vote for the border wall."

The federal government has been in a partial shutdown since Dec. 22 that was prompted by Trump's demand that a spending bill include $5 billion for a wall along the southern border.

Democrats, who will gain control of the House on Thursday when the new Congress begins, have pledged not to approve any funding for the wall.

McConnell said later Wednesday that a House plan to fully reopen the federal government is a "total non-starter," comparing it to "political performance art" that will not be taken up in the Senate.

House Democrats are expected to vote on Thursday on a package to reopen the government. One bill would fund the Department of Homeland Security through Feb. 8. The second would fund the remaining six bills through Sept. 30, the end of the 2019 fiscal year.